logging in or signing up Point Estimation Parameters aSGuest2437 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 943 Category: Education License: All Rights Reserved Like it (0) Dislike it (1) Added: November 03, 2008 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript 7-1 Introduction : 7-1 Introduction The field of statistical inference consists of those methods used to make decisions or to draw conclusions about a population. These methods utilize the information contained in a sample from the population in drawing conclusions. Statistical inference may be divided into two major areas: Parameter estimation Hypothesis testing 7-1 Introduction : Definition 7-1 Introduction 7-1 Introduction : 7-1 Introduction 7-1 Introduction : 7-1 Introduction 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.1 Unbiased Estimators Definition 7-2 General Concepts of Point Estimation : Example 7-1 7-2 General Concepts of Point Estimation 7-2 General Concepts of Point Estimation : Example 7-1 (continued) 7-2 General Concepts of Point Estimation 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.3 Variance of a Point Estimator Definition Figure 7-1 The sampling distributions of two unbiased estimators 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.3 Variance of a Point Estimator Theorem 7-1 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.4 Standard Error: Reporting a Point Estimate Definition 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.4 Standard Error: Reporting a Point Estimate 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation Example 7-2 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation Example 7-2 (continued) 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.6 Mean Square Error of an Estimator Definition 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.6 Mean Square Error of an Estimator 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.6 Mean Square Error of an Estimator Figure 7-2 A biased estimator that has smaller variance than the unbiased estimator 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Definition Definition 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-4 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation 7-3.2 Method of Maximum Likelihood Definition 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-6 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-6 (continued) 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Figure 7-3 Log likelihood for the exponential distribution, using the failure time data. (a) Log likelihood with n = 8 (original data). (b) Log likelihood if n = 8, 20, and 40. 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-9 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-9 (continued) 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Properties of the Maximum Likelihood Estimator 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation The Invariance Property 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-10 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Complications in Using Maximum Likelihood Estimation It is not always easy to maximize the likelihood function because the equation(s) obtained from dL()/d = 0 may be difficult to solve. It may not always be possible to use calculus methods directly to determine the maximum of L(). 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-11 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Figure 7-4 The likelihood function for the uniform distribution in Example 7-11. 7-4 Sampling Distributions : 7-4 Sampling Distributions Statistical inference is concerned with making decisions about a population based on the information contained in a random sample from that population. Definition 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Theorem 7-2: The Central Limit Theorem 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Figure 7-6 Distributions of average scores from throwing dice. [Adapted with permission from Box, Hunter, and Hunter (1978).] Slide 36: Example 7-13 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Figure 7-7 Probability for Example 7-13. 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Definition You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Point Estimation Parameters aSGuest2437 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 943 Category: Education License: All Rights Reserved Like it (0) Dislike it (1) Added: November 03, 2008 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript 7-1 Introduction : 7-1 Introduction The field of statistical inference consists of those methods used to make decisions or to draw conclusions about a population. These methods utilize the information contained in a sample from the population in drawing conclusions. Statistical inference may be divided into two major areas: Parameter estimation Hypothesis testing 7-1 Introduction : Definition 7-1 Introduction 7-1 Introduction : 7-1 Introduction 7-1 Introduction : 7-1 Introduction 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.1 Unbiased Estimators Definition 7-2 General Concepts of Point Estimation : Example 7-1 7-2 General Concepts of Point Estimation 7-2 General Concepts of Point Estimation : Example 7-1 (continued) 7-2 General Concepts of Point Estimation 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.3 Variance of a Point Estimator Definition Figure 7-1 The sampling distributions of two unbiased estimators 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.3 Variance of a Point Estimator Theorem 7-1 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.4 Standard Error: Reporting a Point Estimate Definition 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.4 Standard Error: Reporting a Point Estimate 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation Example 7-2 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation Example 7-2 (continued) 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.6 Mean Square Error of an Estimator Definition 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.6 Mean Square Error of an Estimator 7-2 General Concepts of Point Estimation : 7-2 General Concepts of Point Estimation 7-2.6 Mean Square Error of an Estimator Figure 7-2 A biased estimator that has smaller variance than the unbiased estimator 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Definition Definition 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-4 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation 7-3.2 Method of Maximum Likelihood Definition 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-6 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-6 (continued) 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Figure 7-3 Log likelihood for the exponential distribution, using the failure time data. (a) Log likelihood with n = 8 (original data). (b) Log likelihood if n = 8, 20, and 40. 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-9 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-9 (continued) 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Properties of the Maximum Likelihood Estimator 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation The Invariance Property 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-10 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Complications in Using Maximum Likelihood Estimation It is not always easy to maximize the likelihood function because the equation(s) obtained from dL()/d = 0 may be difficult to solve. It may not always be possible to use calculus methods directly to determine the maximum of L(). 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Example 7-11 7-3 Methods of Point Estimation : 7-3 Methods of Point Estimation Figure 7-4 The likelihood function for the uniform distribution in Example 7-11. 7-4 Sampling Distributions : 7-4 Sampling Distributions Statistical inference is concerned with making decisions about a population based on the information contained in a random sample from that population. Definition 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Theorem 7-2: The Central Limit Theorem 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Figure 7-6 Distributions of average scores from throwing dice. [Adapted with permission from Box, Hunter, and Hunter (1978).] Slide 36: Example 7-13 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Figure 7-7 Probability for Example 7-13. 7-5 Sampling Distributions of Means : 7-5 Sampling Distributions of Means Definition